{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Математическая статистика"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statistics import multimode\n",
    "\n",
    "import numpy as np\n",
    "import scipy.stats as sps\n",
    "import ipywidgets as widgets\n",
    "import matplotlib.pyplot as plt\n",
    "import PyPDF2\n",
    "import re\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Номер в группе 14\n"
     ]
    }
   ],
   "source": [
    "N = 14\n",
    "print(f'Номер в группе {N}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача.** Получение и визуализация выборки заданного <i><u>дискретного</u></i> распределения "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>Шаг 1.</i> \n",
    "\n",
    "Из списка дискретных случайных величин выберите случайные величины с номером $N$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "variants = np.array([\n",
    "    1, 4, 6, 7, 12, 27, 28, 29.5, 30, 31.9, 32, \n",
    "    39, 39.1, 39.2, 39.3, 39.4, 40, 41, 42, 50\n",
    "])\n",
    "freq = np.array([2, 3, 4, 5, 6, 7, 7, 5, 6, 7, 8, 10, 25, 1, 1, 1, 1, 1, 4, 1]) / 105"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Визуализируем входные данные для наглядности распределения:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Случайная величина: Вероятностная мера\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{1.0: 0.01904761904761905,\n",
       " 4.0: 0.02857142857142857,\n",
       " 6.0: 0.0380952380952381,\n",
       " 7.0: 0.047619047619047616,\n",
       " 12.0: 0.05714285714285714,\n",
       " 27.0: 0.06666666666666667,\n",
       " 28.0: 0.06666666666666667,\n",
       " 29.5: 0.047619047619047616,\n",
       " 30.0: 0.05714285714285714,\n",
       " 31.9: 0.06666666666666667,\n",
       " 32.0: 0.0761904761904762,\n",
       " 39.0: 0.09523809523809523,\n",
       " 39.1: 0.23809523809523808,\n",
       " 39.2: 0.009523809523809525,\n",
       " 39.3: 0.009523809523809525,\n",
       " 39.4: 0.009523809523809525,\n",
       " 40.0: 0.009523809523809525,\n",
       " 41.0: 0.009523809523809525,\n",
       " 42.0: 0.0380952380952381,\n",
       " 50.0: 0.009523809523809525}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = dict(zip(variants, freq))\n",
    "plt.plot(variants, freq, '-o')\n",
    "plt.show()\n",
    "\n",
    "print('Случайная величина: Вероятностная мера')\n",
    "table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>Шаг 2.</i>\n",
    "\n",
    "Для данных случайных величин, создайте функцию распределения вашей случайной величины (если необходимо)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Сумма частот -0.9999999999999997, что не равно 1 из-за дискретности ЭВМ, поэтому выполняем нормализацию.\n",
      "Снова суммируем и получаем: 1.0\n"
     ]
    }
   ],
   "source": [
    "summary = sum(freq)\n",
    "\n",
    "print(f'Сумма частот -{summary}, что не равно 1 из-за дискретности ЭВМ, поэтому выполняем нормализацию.')\n",
    "\n",
    "freq_norm = list(map(lambda p: p / summary, freq))\n",
    "\n",
    "print(f'Снова суммируем и получаем: {sum(freq_norm)}')\n",
    "\n",
    "distribution = sps.rv_discrete(values = (variants, freq_norm))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>Шаг 3.</i>\n",
    "\n",
    "Создайте выборку длины 100 для вашей случайной величины. Напечатайте массив частот и массив вариант"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "size = 100\n",
    "sample = distribution.rvs(size = size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([39.1, 40. , 39. , 31.9, 39.1, 28. , 30. , 28. , 39.1, 39. , 39.1,\n",
       "       27. ,  7. , 31.9,  7. , 39. , 32. , 39.1, 39. , 29.5,  7. ,  6. ,\n",
       "       28. , 42. , 41. , 39. ,  1. ,  6. , 28. , 31.9, 39. , 39.3, 30. ,\n",
       "       12. , 30. , 31.9, 39.1, 28. , 31.9, 39. , 39.4, 32. , 39. , 31.9,\n",
       "        1. , 31.9, 31.9,  6. , 12. , 41. , 42. , 28. , 39.3, 12. , 31.9,\n",
       "        4. , 39. ,  4. , 29.5, 39. , 39.1, 40. , 39. , 39.1, 39. ,  4. ,\n",
       "       39.1,  7. , 39.1, 28. , 39. , 32. , 12. , 40. , 39.1, 27. , 39.1,\n",
       "        6. , 28. , 32. , 29.5, 39.1, 27. , 28. , 50. , 41. , 39.1, 27. ,\n",
       "       28. , 41. , 31.9, 39.1, 40. ,  6. , 39.1, 29.5, 30. , 28. , 39.1,\n",
       "       42. ])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1. ,  4. ,  6. ,  7. , 12. , 27. , 28. , 29.5, 30. , 31.9, 32. ,\n",
       "       39. , 39.1, 39.2, 39.3, 39.4, 40. , 41. , 42. , 50. ])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variants"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>Шаг 4.</i>\n",
    "\n",
    "Опишите вашу выборку: объем, экстремальные статистики, медиана, мода, размах, среднее, дисперсия, эксцесс и асимметрия. Сравните с результатами калькуляции функциями из пакета Stats https://docs.scipy.org/doc/scipy/reference/stats.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "from collections import OrderedDict\n",
    "\n",
    "counter = Counter(sample)\n",
    "oredered = OrderedDict(sorted(counter.items(), key = lambda t: t[0]))\n",
    "\n",
    "variants = oredered.keys()\n",
    "freq = oredered.values()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_median(array):\n",
    "    middle = len(array) / 2.\n",
    "    if (middle % 1 == 0):\n",
    "        return (array[int(middle) + 1] + array[int(middle)]) / 2\n",
    "    else:\n",
    "        return array[int(middle)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Объем выборки: 100\n",
      "Минимум, максимум: (1.0, 50.0)\n",
      "Среднее: 30.107\n",
      "Дисперсия: 147.19257676767677\n",
      "Размах: 49.0\n",
      "Ассиметрия: -1.1378815903953958\n",
      "Эксцесс: 0.11493500615842711\n",
      "II момент: 145.720651\n",
      "III момент: -2001.6066040139997\n",
      "IV момент: 66144.1127060386\n",
      "Медиана: 35.0\n",
      "Мода: [39.1]\n"
     ]
    }
   ],
   "source": [
    "print('Объем выборки:', len(sample))\n",
    "print('Минимум, максимум:', (min(sample), max(sample)))\n",
    "\n",
    "avg = sum(sample) / size\n",
    "\n",
    "def moment(n, length = size, array = sample):\n",
    "    return np.sum(list(map(lambda x: (x - avg) ** n, array))) / length\n",
    "\n",
    "print('Среднее:', avg)\n",
    "print('Дисперсия:', moment(2, length = size - 1))\n",
    "print('Размах:', max(sample) - min(sample))\n",
    "\n",
    "print('Ассиметрия:', moment(3) / moment(2) ** (3 / 2))\n",
    "print('Эксцесс:', moment(4) / (moment(2) ** 2) - 3)\n",
    "\n",
    "print('II момент:', moment(2))\n",
    "print('III момент:', moment(3))\n",
    "print('IV момент:', moment(4))\n",
    "\n",
    "print('Медиана:', find_median(list(sample)))\n",
    "print('Мода:', multimode(list(sample)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Получаем значения через функции из пакета Stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Объем выборки: 100\n",
      "Минимум, максимум: (1.0, 50.0)\n",
      "Среднее: 30.107000000000003\n",
      "Дисперсия: 147.19257676767677\n",
      "Ассиметрия: -1.137881590395397\n",
      "Эксцесс: 0.114935006158428\n",
      "II момент: 145.720651\n",
      "III момент: -2001.6066040140015\n",
      "IV момент: 66144.11270603862\n",
      "Мода: 39.1 количество: 17\n"
     ]
    }
   ],
   "source": [
    "obj = sps.describe(sample)\n",
    "\n",
    "print('Объем выборки:', obj.nobs)\n",
    "print('Минимум, максимум:', obj.minmax)\n",
    "print('Среднее:', obj.mean)\n",
    "print('Дисперсия:', obj.variance)\n",
    "\n",
    "print('Ассиметрия:', obj.skewness)\n",
    "print('Эксцесс:', obj.kurtosis)\n",
    "\n",
    "print('II момент:', sps.moment(sample, moment = 2))\n",
    "print('III момент:', sps.moment(sample, moment = 3))\n",
    "print('IV момент:', sps.moment(sample, moment = 4))\n",
    "\n",
    "mode = sps.mode(sample, keepdims = False)\n",
    "\n",
    "print(f'Мода: {mode.mode} количество: {mode.count}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Как мы видим, все характеристики совпадают"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>Шаг 5.</i>\n",
    "\n",
    "Создайте полигон частот и гистограмму для каждой выборки\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Список количества каждой случайной величины в выборке"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({39.1: 17,\n",
       "         39.0: 13,\n",
       "         28.0: 11,\n",
       "         31.9: 10,\n",
       "         6.0: 5,\n",
       "         40.0: 4,\n",
       "         30.0: 4,\n",
       "         27.0: 4,\n",
       "         7.0: 4,\n",
       "         32.0: 4,\n",
       "         29.5: 4,\n",
       "         41.0: 4,\n",
       "         12.0: 4,\n",
       "         42.0: 3,\n",
       "         4.0: 3,\n",
       "         1.0: 2,\n",
       "         39.3: 2,\n",
       "         39.4: 1,\n",
       "         50.0: 1})"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(variants, freq, color = 'blue', lw = 3, label = 'полигон частот')\n",
    "plt.hist(sample, 3 * size, color = 'red', label = 'гистограмма')\n",
    "plt.legend()\n",
    "\n",
    "plt.xlabel('Случайные величины')\n",
    "plt.ylabel('Частота')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача.** Получение и визуализация выборки заданного <i><u>непрерывного</u></i> распределения."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>Шаг 1.</i> \n",
    "\n",
    "Из списка непрерывных случйных величин выберите с номером $N$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Вариант 14\n",
      "X распределен по закону N(2, 5)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "reader = PyPDF2.PdfReader('datasets/Непрерывные величны, практикум 1.pdf')\n",
    "\n",
    "message = 'Вариант '\n",
    "variant = f'Вариант {N}'\n",
    "\n",
    "for i in range(len(reader.pages)):\n",
    "    \n",
    "    text = reader.pages[i].extract_text()\n",
    "    \n",
    "    if variant in text:\n",
    "        index = text.index(str(N))\n",
    "        \n",
    "        end = index\n",
    "        while not end == len(text) and not text[end] == 'В':\n",
    "            message += text[end]\n",
    "            end += 1\n",
    "        break\n",
    "\n",
    "print(message)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "μ = 2, σ_square = 5\n"
     ]
    }
   ],
   "source": [
    "parameters = re.findall(r'\\w+', message)\n",
    "\n",
    "μ = int(parameters[-2])\n",
    "σ_square = int(parameters[-1])\n",
    "\n",
    "print(f'μ = {μ}, σ_square = {σ_square}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>Шаг 2.</i>\n",
    "\n",
    "Для данных случайных величин, создайте функцию распределения вашей случайной величины (если необходимо)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Первые 12 значений выборки:\n",
      " [1.9923461  2.10358144 1.01799801 0.99960563 3.10171659 2.25491426\n",
      " 0.68907897 1.82574993 0.5925043  4.87711938 2.37904562 3.04589457]\n"
     ]
    }
   ],
   "source": [
    "normal = sps.norm.rvs(size = size, loc = μ, scale = np.sqrt(σ_square))\n",
    "show_count = 12\n",
    "\n",
    "print(f'Первые {show_count} значений выборки:\\n', normal[:show_count])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>Шаг 3.</i>\n",
    "\n",
    "Создайте выборку длины 100 для вашей случайной величины. Напечатайте массив частот и массив вариант"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Массив вариант: \n",
      "dict_keys([-2.2442396162631724, -1.5378287529835495, -0.8314178897039268, -0.12500702642430417, 0.5814038368553187, 1.2878147001349416, 1.994225563414564, 2.700636426694187, 3.40704728997381, 4.113458153253433, 4.8198690165330556, 5.526279879812678, 6.2326907430923, 6.939101606371924, 7.645512469651545]) \n",
      "\n",
      " Массив частот: \n",
      "dict_values([3, 3, 6, 9, 18, 10, 15, 11, 9, 5, 5, 2, 2, 1, 1])\n"
     ]
    }
   ],
   "source": [
    "bin_count = 15\n",
    "\n",
    "bins = np.linspace(min(normal), max(normal), num = bin_count)\n",
    "            \n",
    "counter = Counter(np.digitize(normal, bins))\n",
    "oredered = OrderedDict(sorted(counter.items(), key = lambda t: t[0]))\n",
    "\n",
    "data = dict.fromkeys(bins, 0)\n",
    "\n",
    "for key, count in oredered.items():\n",
    "    data[bins[key - 1]] = count\n",
    "\n",
    "print(f'Массив вариант: \\n{data.keys()}', '\\n\\n' , f'Массив частот: \\n{data.values()}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>Шаг 4.</i>\n",
    "\n",
    "Опишите вашу выборку: объем, экстремальные статистики, медиана, мода, размах, среднее, дисперсия, эксцесс и асимметрия. Сравните с результатами калькуляции функциями из пакета Stats https://docs.scipy.org/doc/scipy/reference/stats.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Объем выборки: 100\n",
      "Минимум, максимум: (-2.2442396162631724, 7.645512469651545)\n",
      "Среднее: 2.1298428196677017\n",
      "Дисперсия: 4.206621987952504\n",
      "Размах: 9.889752085914719\n",
      "Ассиметрия: 0.3537183481205304\n",
      "Эксцесс: -0.15914961042483045\n",
      "II момент: 4.1645557680729794\n",
      "III момент: 3.006149752942509\n",
      "IV момент: 49.270359029547556\n",
      "Медиана: 2.2402148666676966\n",
      "Мода (ограничение на 3 значения): [1.9923460954084011, 2.1035814434602536, 1.0179980073211405]\n"
     ]
    }
   ],
   "source": [
    "print('Объем выборки:', len(normal))\n",
    "print('Минимум, максимум:', (min(normal), max(normal)))\n",
    "\n",
    "avg = sum(normal) / size\n",
    "\n",
    "print('Среднее:', avg)\n",
    "print('Дисперсия:', moment(2, length = size - 1, array = normal))\n",
    "print('Размах:', max(normal) - min(normal))\n",
    "\n",
    "print('Ассиметрия:', moment(3, array = normal) / moment(2, array = normal) ** (3 / 2))\n",
    "print('Эксцесс:', moment(4, array = normal) / (moment(2, array = normal) ** 2) - 3)\n",
    "\n",
    "print('II момент:', moment(2, array = normal))\n",
    "print('III момент:', moment(3, array = normal))\n",
    "print('IV момент:', moment(4, array = normal))\n",
    "\n",
    "print('Медиана:', find_median(list(normal)))\n",
    "print('Мода (ограничение на 3 значения):', multimode(list(normal))[:3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Получаем значения через функции из пакета Stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Объем выборки: 100\n",
      "Минимум, максимум: (-2.2442396162631724, 7.645512469651545)\n",
      "Среднее: 2.129842819667702\n",
      "Дисперсия: 4.206621987952505\n",
      "Ассиметрия: 0.35371834812052966\n",
      "Эксцесс: -0.15914961042483045\n",
      "II момент: 4.1645557680729794\n",
      "III момент: 3.0061497529425028\n",
      "IV момент: 49.270359029547556\n",
      "Мода: -2.2442396162631724 количество: 1\n"
     ]
    }
   ],
   "source": [
    "obj = sps.describe(normal)\n",
    "\n",
    "print('Объем выборки:', obj.nobs)\n",
    "print('Минимум, максимум:', obj.minmax)\n",
    "print('Среднее:', obj.mean)\n",
    "print('Дисперсия:', obj.variance)\n",
    "\n",
    "print('Ассиметрия:', obj.skewness)\n",
    "print('Эксцесс:', obj.kurtosis)\n",
    "\n",
    "print('II момент:', sps.moment(normal, moment = 2))\n",
    "print('III момент:', sps.moment(normal, moment = 3))\n",
    "print('IV момент:', sps.moment(normal, moment = 4))\n",
    "\n",
    "mode = sps.mode(normal, keepdims = False)\n",
    "\n",
    "print(f'Мода: {mode.mode} количество: {mode.count}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Как мы видим, все характеристики совпадают"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>Шаг 5.</i>\n",
    "\n",
    "Создайте полигон частот и гистограмму для каждой выборки\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Список количества каждой случайной величины в выборке"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(data.keys(), data.values(), color = 'blue', lw = 3, label = 'полигон частот')\n",
    "plt.hist(normal, bin_count, color = 'yellow', label = 'гистограмма')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
